X,Y,Z are consecutive integers. N = x + y + z . Is N divisible by 10?
(1) x + z is a multiple of 10
(2) y is a multiple of 10
(1) x + z is a multiple of 10
(2) y is a multiple of 10
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67) is n divisible
Source: Beat The GMAT — Data Sufficiency |
IMO (B)
Reason: if x,y,z are 4,5,6 then 4+6 (x+z) is a multiple of 10 but 4+5+6=15 is not divisible by 10. Hence (1) is insufficient.
Reason: if x,y,z are 4,5,6 then 4+6 (x+z) is a multiple of 10 but 4+5+6=15 is not divisible by 10. Hence (1) is insufficient.
X,Y,Z are consecutive integers i.e X,Y,Z are a-1,a,a+1..not in order
So N=3a..if we can definitely say a is a multiple of 10 or not question can be answered
From 1
X+Z=10k
this says X and Z has to be a+1 and a-1 and
a-1+a+1=10k or 2a=10k or a=5k...a may or may not be multiple of 10
option 2
Y is a multiple of 10..hence either of a-1,a,a+1 is a multiple of 10
if Y =a..then N is also multiple of 10 else if Y =a+1 or a-1..N is not a multiple of 10...insufficient
combining
Y =a and Y is a multiple of 10 hence N is multiple of 10
Ans option C
Please confirm the OA.
So N=3a..if we can definitely say a is a multiple of 10 or not question can be answered
From 1
X+Z=10k
this says X and Z has to be a+1 and a-1 and
a-1+a+1=10k or 2a=10k or a=5k...a may or may not be multiple of 10
option 2
Y is a multiple of 10..hence either of a-1,a,a+1 is a multiple of 10
if Y =a..then N is also multiple of 10 else if Y =a+1 or a-1..N is not a multiple of 10...insufficient
combining
Y =a and Y is a multiple of 10 hence N is multiple of 10
Ans option C
Please confirm the OA.
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
St 1 :ern5231 wrote:X,Y,Z are consecutive integers. N = x + y + z . Is N divisible by 10?
(1) x + z is a multiple of 10
(2) y is a multiple of 10
x + z is a multiple of 10
Let us plug in numbers:
x=19 y=20 z=21
x+z= 19+21 is a multiple of 10 .
And so N is a Divisible by 10.
St 2:y is a multiple of 10
Again plug in numbers: y=30
x=29,z=31
Now N= 29+30+31
N=90 which is divisible by 10.
IMO D
Hmm..I think you have missed few optionsgmatmachoman wrote:St 1 :ern5231 wrote:X,Y,Z are consecutive integers. N = x + y + z . Is N divisible by 10?
(1) x + z is a multiple of 10
(2) y is a multiple of 10
x + z is a multiple of 10
Let us plug in numbers:
x=19 y=20 z=21
x+z= 19+21 is a multiple of 10 .
And so N is a Divisible by 10.
St 2:y is a multiple of 10
Again plug in numbers: y=30
x=29,z=31
Now N= 29+30+31
N=90 which is divisible by 10.
IMO D
In condition 1
let us take x=4,y=5,z=6..x+z=10..multiple of 10
x+y+z=15..non multiple of 10
In condition 2
y=10
then x=9 z=11...or x=11,z=12 or x=8,z=9...
What say?
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
Since X, Y, Z are consecutive integers
So Let Y = X + 1 and Z = X + 2
=> N = X + X + 1 + X + 2
N = 3(X + 1)
1) x + z is a multiple of 10 .
=> X + X + 2 is multiple of 10
=> 2(X+1) is multiple of 10
=> (X+1) is multiple of 5.
This means N is multiple of 5(and also 3) because N = 3(X+1)
2) y is a multiple of 10
=> (X+1) is multiple of 10
This certainly means N is multiple of 10 because N = 3(X+1)
So[spoiler] 2)[/spoiler] alone is sufficient hence IMO ans is B
So Let Y = X + 1 and Z = X + 2
=> N = X + X + 1 + X + 2
N = 3(X + 1)
1) x + z is a multiple of 10 .
=> X + X + 2 is multiple of 10
=> 2(X+1) is multiple of 10
=> (X+1) is multiple of 5.
This means N is multiple of 5(and also 3) because N = 3(X+1)
2) y is a multiple of 10
=> (X+1) is multiple of 10
This certainly means N is multiple of 10 because N = 3(X+1)
So[spoiler] 2)[/spoiler] alone is sufficient hence IMO ans is B
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nikhilkatira
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amitverma22 wrote:Since X, Y, Z are consecutive integers
So Let Y = X + 1 and Z = X + 2
=> N = X + X + 1 + X + 2
N = 3(X + 1)
1) x + z is a multiple of 10 .
=> X + X + 2 is multiple of 10
=> 2(X+1) is multiple of 10
=> (X+1) is multiple of 5.
This means N is multiple of 5(and also 3) because N = 3(X+1)
2) y is a multiple of 10
=> (X+1) is multiple of 10
This certainly means N is multiple of 10 because N = 3(X+1)
So[spoiler] 2)[/spoiler] alone is sufficient hence IMO ans is B
let x = m, then y = m+1 and z = m+2
implying that N = x+y+z = 3m + 3 or 3(m+1)
is 3m + 3 = 10k?
1) x+z = 10r implying 2m+2 = 10r insufficient!
2) y = 10q implying m+1 = 10q insufficient!
combine 1 and 2: x+z + y = (2m+2) + (m+1) = 10r+10q
this in essence means 3m+3 = 10 (r+q)
ANSWER (C)
[email protected] wrote:amitverma22 wrote:Since X, Y, Z are consecutive integers
So Let Y = X + 1 and Z = X + 2
=> N = X + X + 1 + X + 2
N = 3(X + 1)
1) x + z is a multiple of 10 .
=> X + X + 2 is multiple of 10
=> 2(X+1) is multiple of 10
=> (X+1) is multiple of 5.
This means N is multiple of 5(and also 3) because N = 3(X+1)
2) y is a multiple of 10
=> (X+1) is multiple of 10
This certainly means N is multiple of 10 because N = 3(X+1)
So[spoiler] 2)[/spoiler] alone is sufficient hence IMO ans is B
let x = m, then y = m+1 and z = m+2
implying that N = x+y+z = 3m + 3 or 3(m+1)
is 3m + 3 = 10k?
1) x+z = 10r implying 2m+2 = 10r insufficient!
2) y = 10q implying m+1 = 10q insufficient!
combine 1 and 2: x+z + y = (2m+2) + (m+1) = 10r+10q
this in essence means 3m+3 = 10 (r+q)
ANSWER (C)
Taking your case 2)
y = 10q implying m+1 = 10q
This implies 3(m + 1) = 3*10q
This implies 3m + 3 = 10*(3q)
Hence 3m + 3 is definitely multiple of 10.
So 2) is sufficient to answer the question
i see; i agree with you.amitverma22 wrote:[email protected] wrote:amitverma22 wrote:Since X, Y, Z are consecutive integers
So Let Y = X + 1 and Z = X + 2
=> N = X + X + 1 + X + 2
N = 3(X + 1)
1) x + z is a multiple of 10 .
=> X + X + 2 is multiple of 10
=> 2(X+1) is multiple of 10
=> (X+1) is multiple of 5.
This means N is multiple of 5(and also 3) because N = 3(X+1)
2) y is a multiple of 10
=> (X+1) is multiple of 10
This certainly means N is multiple of 10 because N = 3(X+1)
So[spoiler] 2)[/spoiler] alone is sufficient hence IMO ans is B
let x = m, then y = m+1 and z = m+2
implying that N = x+y+z = 3m + 3 or 3(m+1)
is 3m + 3 = 10k?
1) x+z = 10r implying 2m+2 = 10r insufficient!
2) y = 10q implying m+1 = 10q insufficient!
combine 1 and 2: x+z + y = (2m+2) + (m+1) = 10r+10q
this in essence means 3m+3 = 10 (r+q)
ANSWER (C)
Taking your case 2)
y = 10q implying m+1 = 10q
This implies 3(m + 1) = 3*10q
This implies 3m + 3 = 10*(3q)
Hence 3m + 3 is definitely multiple of 10.
So 2) is sufficient to answer the question
x,y & z are consec nos.ern5231 wrote:X,Y,Z are consecutive integers. N = x + y + z . Is N divisible by 10?
(1) x + z is a multiple of 10
(2) y is a multiple of 10
so 2y = x+z
1) x+z = 10a , y = 5a
N= 15a divisible by 5 not necessarily 10 . Insuff
2) y = 10 a , x+z = 20a
N = 30a so it is divisible by 10. Suff
IMO B
I'm reposting the following
In condition 1
let us take x=4,y=5,z=6..x+z=10..multiple of 10
x+y+z=15..non multiple of 10
In condition 2
y=10
then x=9 z=11...or x=11,z=12 or x=8,z=9...
What say?
My question then,
now when a questions states numbers x, y, z are consecutive numbers, does it necessarily mean that x is the smallest, y is the middle number and z is the largest?
In condition 1
let us take x=4,y=5,z=6..x+z=10..multiple of 10
x+y+z=15..non multiple of 10
In condition 2
y=10
then x=9 z=11...or x=11,z=12 or x=8,z=9...
What say?
My question then,
now when a questions states numbers x, y, z are consecutive numbers, does it necessarily mean that x is the smallest, y is the middle number and z is the largest?
Good pointlayzzer wrote:I'm reposting the following
My question then,
now when a questions states numbers x, y, z are consecutive numbers, does it necessarily mean that x is the smallest, y is the middle number and z is the largest?
1) x+z is a multiple of 10
since sum of two consecutive nos cannot be multiple of 10, x and z are not consecutive nos. So x and z are the smallest and the largest nos. in the series or vice versa. But it is not Suff to say whether N is a multiple of 10.
2) y is multiple of 10. but y can be the first , middle or the last number. Only if y is the middle value than N is a multiple of 10. Insufficient.
Combining it is possible to deduce that y is the middle no. Rest is the same.
OK IMHO it is C.
